Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods

Siegert pseudostates are purely outgoing states at some fixed point expanded over a finite basis. With discretized variables, they provide an accurate description of scattering in the s wave for short-range potentials with few basis states. The R-matrix method combined with a Lagrange basis, i.e. functions which vanish at all points of a mesh but one, leads to simple mesh-like equations which also allow an accurate description of scattering. These methods are shown to be exactly equivalent for any basis size, with or without discretization. The comparison of their assumptions shows how to accurately derive poles of the scattering matrix in the R-matrix formalism and suggests how to extend the Siegert-pseudostate method to higher partial waves. The different concepts are illustrated with the Bargmann potential and with the centrifugal potential. A simplification of the R-matrix treatment can usefully be extended to the Siegert-pseudostate method.Comment: 19 pages, 1 figur

Vertically integrated spot-size converter in AlGaAs-GaAs

We report on the demonstration of a spot size converter (SSC) for monolithic photonic integration at a wavelength of 850 nm on a GaAs substrate. We designed and fabricated a dual-waveguide AlGaAs chip. The design consists of a lower waveguide layer for efficient end-fire coupling to a single-mode fiber, an upper waveguide layer for high refractive index contrast waveguides, and a vertical SSC to connect the two waveguide layers. We measured a SSC conversion efficiency of 91% (or −0.4  dB) between the upper and lower waveguide layers for the TE mode at a wavelength of 850 nm

Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Pseudo-time Schroedinger equation with absorbing potential for quantum scattering calculations

The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time correlation function. An efficient formula for Green's function matrix elements is also derived. Since the exact propagation up to time 2t can be done with only t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.Comment: 9 page

Vertically integrated spot-size converter in AlGaAs-GaAs

We report on the demonstration of a spot size converter (SSC) for monolithic photonic integration at a wavelength of 850 nm on a GaAs substrate. We designed and fabricated a dual-waveguide AlGaAs chip. The design consists of a lower waveguide layer for efficient end-fire coupling to a single-mode fiber, an upper waveguide layer for high refractive index contrast waveguides, and a vertical SSC to connect the two waveguide layers. We measured a SSC conversion efficiency of 91% (or −0.4  dB) between the upper and lower waveguide layers for the TE mode at a wavelength of 850 nm

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure

The Hyperspherical Four-Fermion Problem

The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behavior of superconductors, fermionic superfluids, and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulas that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS-BEC crossover problem Derivations and relevant formulas are also included for the calculation of challenging few-body processes such as recombination.Comment: 66 pages, 33 figure